Piezoelectric transducers have been used to harvest mechanical energy for micro-power applications. FIG. 1 is an illustrative drawing showing an example piezoelectric energy harvesting system. A piezoelectric transducer is electrically coupled to a rectifier circuit, which is coupled to an energy storage element and a load that draws energy from the storage element. The piezoelectric transducer converts the vibration mechanical energy into AC electrical energy which is then rectified into DC energy by the rectifier and stored into the storage element to provide a supply voltage for the load circuitry. A maximum power point tracking (MPPT) typically is used in an energy harvesting system to achieve the maximum power from the piezoelectric transducer no matter how the environment changes. MPPT based upon resistive matching has been used in piezoelectric energy harvesting systems. N. Kong et al., “Resistive Impedance Matching Circuit for Piezoelectric Energy Harvesting,” Journal of intelligent material systems and structures, vol. 21, pp. 1293-1302, September 2010; and C. Lu et al., “Vibration Energy Scavenging System With Maximum Power Tracking for Micropower Applications,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 19, no. 11, pp. 2109-2119, November 2011. In normal operation, the rectifier's output voltage is controlled to be half of the open voltage of the piezoelectric transducer such that the rectifier's input resistance matches with the internal resistance of the piezoelectric transducer. The rectifier's output is controlled by adjusting the duty ratio of the followed DC-DC. Usually, the piezoelectric transducer has a non-negligible parasitic capacitance that traps major power, and as a result, only minor power flows to the loading. Thus, resistive matching based MPPT typically does not provide optimal power harvesting.
As a consequence, conjugate matching is required to avoid power trapping in the reactance of a piezoelectric transducer. FIG. 2A is an illustrative drawing representing a model of a piezoelectric transducer with cantilever structure. The model includes models of both mechanical and electrical characteristics of the transducer shown separated by a vertical dashed line. On the mechanical side, a mechanical vibration source VSm imparts mechanical vibration to the transducer. The piezoelectric transducer includes a mechanical inductor Lm and a mechanical capacitor Cm, which represent the equivalent mass and stiffness of the transducer, respectively. The piezoelectric transducer also includes a mechanical resistor Rm, which represents mechanical damping. The transformer represents the coupling between the mechanical domain and the electrical domain. On the electrical side, the piezoelectric transducer has a non-negligible parasitic capacitor CP.
FIG. 2B is an illustrative drawing representing a simplified version of the piezoelectric transducer model of FIG. 2A. During operation of the piezoelectric transducer at resonant frequency, the mechanical reactances Lm and Cm cancel each other out, and Rm and CP remain. In piezoelectric energy harvesting, if the electrical load (not shown) is purely resistive, then much of the electrical power coupled from the mechanical side will be trapped in the capacitance CP and then be reflected back into the mechanical domain and dissipated by the Rm. The electrical load may include rectifier circuitry or other circuits, for example. Conjugate matching using an inductor (not shown) has been used to compensate for the parasitic capacitive reactance CP of the piezoelectric transducer. However, due to typical low frequency operation of the piezoelectric transducer, usually in the range of approximately 10 to 100 Hertz, a physically large inductor was required, which can be impractical in actual applications. See, S. Roundy, P. K. Wright, J. Rabaey, “A study of low level vibrations as a power source for wireless sensor nodes,” Computer Communications, vol. 26, pp. 1131-1144, 2003.
Bias flipping technique has been used to achieve impedance matching using a small inductance to achieve improved energy harvesting from a piezoelectric transducer. See, Y. K. Ramadass, and A. P. Chandrakasan, “An Efficient Piezoelectric Energy Harvesting Interface Circuit Using a Bias-Flip Rectifier and Shared Inductor,” IEEE Journal of Solid-State Circuits, vol. 45, no. 1, pp. 189-204, January 2010; Y. S. Yuk, et al., “An Energy Pile-Up Resonance Circuit Extracting Maximum 422% Energy from Piezoelectric Material in a Dual-Source Energy-Harvesting Interface,” ISSCC, 2014; and J. Zhao et al., “Bias-Flip Technique for Frequency Tuning of Piezo-Electric Energy Harvesting Devices,” Journal of Low Power Electronics and Applications, vol. 3, pp. 194-214, April, 2013. FIG. 3A is an illustrative drawing representing a parasitic capacitance portion of a piezoelectric transducer and an impedance matching circuit used to achieve impedance matching through a bias flip technique. A stimulated current source IS is coupled across the terminals of a parasitic capacitance CP. The current source IS is stimulated by mechanical vibration of the transducer, which is stimulated by an external vibration source (not shown). A switch controlled inductor L is coupled in parallel to shunt the parasitic capacitance CP. VS represents a stimulated voltage across the capacitance CP that is stimulated by the vibration source. A switch circuit alternately opens and closes to controllably decouple and couple the shunt coupling between the inductor L and the capacitance CP.
FIG. 3B is an illustrative drawing showing waveforms representing a bias flip process to achieve impedance matching using the switched inductance in the circuit of FIG. 3A. Waveform IS represents a stimulated current, having a sinusoidal shape. Waveform VS represents the stimulated voltage output of the piezoelectric transducer without bias flipping. Stated differently, waveform VS represents the stimulated voltage output, which if the switch were always open, also would have a sinusoidal shape that is phase shifted by 90 degrees from IS. Waveform SW represents a sequence of switch transitions, from open to close and from close to open. Waveform VSbp represents a resulting stimulated voltage with bias flip due to alternately opening and closing the switch. Referring to waveform SW, the switch closes at VS peak, and remains closed for long enough for the inductor and the parasitic capacitance to be resonant so as to achieve bias flip and then opens again. The switch also closes at each VS valley, and remains closed for long enough for the bias flip to occur and then open again. Thus, bias flipping of the VSbp waveform occurs at each VS peak and each VS valley. It will be appreciated, therefore, that the VSbp waveform bias flips at one-half cycle intervals. The inductor L is selected to have a small value so that energy resonates between CP and L at a high frequency. It can be seen that in steady state, the resulting waveform VSbp is substantially in phase with IS indicating that impedances L and CP are matched resulting in cancellation of the reactance CP. Thus, bias flip achieves impedance matching using a smaller more practical switched inductor L, which releases energy that otherwise, would be trapped by parasitic capacitance CP. See, J. Zhao et al., Supra.